energies

Article

A Novel Approach for the Determination of SorptionEquilibria and Sorption Enthalpy Used for MOFAluminium Fumarate with Water

Eric Laurenz 1,2,* , Gerrit Füldner 1,*, Lena Schnabel 1 and Gerhard Schmitz 2

1 Department Heating and Cooling Technologies, Fraunhofer Institute for Solar Energy Systems ISE,Heidenhofstr. 2, 79110 Freiburg, Germany; lena.schnabel@ise.fraunhofer.de

2 Institute of Engineering Thermodynamics, Hamburg University of Technology, Denickestr. 17,21073 Hamburg, Germany; schmitz@tuhh.de

* Correspondence: eric.laurenz@ise.fraunhofer.de (E.L.); gerrit.fueldner@ise.fraunhofer.de (G.F.)

Received: 19 May 2020; Accepted: 9 June 2020; Published: 11 June 2020�����������������

Abstract: Adsorption chillers offer an environmentally friendly solution for the valorisation ofwaste or solar heat for cooling demands. A recent application is high efficiency data centre cooling,where heat from CPUs is used to drive the process, providing cooling for auxiliary loads. The metalorganic framework aluminium fumarate with water is potentially a suitable material pair for this lowtemperature driven application. A targeted heat exchanger design is a prerequisite for competitiveness,requiring, amongst other things, a sound understanding of adsorption equilibria and adsorptionenthalpy. A novel method is employed for their determination based on small isothermal andisochoric state changes, applied with an apparatus developed initially for volume swing frequencyresponse measurement, to samples with a binder-based adsorbent coating. The adsorption enthalpyis calculated through the Clausius–Clapeyron equation from the obtained slopes of the isothermand isobar, while the absolute uptake is determined volumetrically. The isotherm confirms thestep-like form known for aluminium fumarate, with a temperature dependent inflection point atprel ≈ 0.25, 0.28 and 0.33 for 30 ◦C, 40 ◦C and 60 ◦C. The calculated differential enthalpy of adsorptionis 2.90 ± 0.05 MJ/kg (52.2 ± 1.0 kJ/mol) on average, which is about 10–15% higher than expected by asimple Dubinin approximation.

Keywords: adsorption equilibrium; adsorption enthalpy; heat of adsorption; metal organicframework; aluminum fumarate; coating; adsorption; cooling; heat pump; heat transformation

1. Introduction

Adsorption chillers offer an environmentally friendly solution for the valorisation of waste orsolar heat for cooling demands. The working principle allows a simple, robust, and scalable design.Adsorption chillers and heat pumps have been applied successfully for different applications, like solarthermal cooling of buildings [1], gas adsorption heat pumps [2,3] and more [4,5]. A possible applicationthat has attracted rising interest in recent years is the provision of data centre cooling driven by heatyielded from water cooled CPUs. Current high-performance CPUs allow cooling water temperaturesof up to 60 ◦C or more [6,7], that can be used to drive adsorption chillers.

An adsorption chiller (Figure 1) consists of two adsorption heat exchangers, a condenser, and anevaporator, in a pure working fluid atmosphere. If temperatures below 0 ◦C can be excluded, usuallywater is used as working fluid, due to its high evaporation enthalpy. The adsorption heat exchangers(Ad-HX) have a heat transfer fluid on the primary and a stationary adsorbent material or compositeon the secondary side. The process is cyclic: In the first half-cycle, the CPU’s waste heat is usedto regenerate the first Ad-HX. The desorbed working fluid is condensed in the condenser which is

Energies 2020, 13, 3003; doi:10.3390/en13113003 www.mdpi.com/journal/energies

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cooled to the ambient at, e.g., 30 ◦C. In the second half-cycle, working fluid is adsorbed on the Ad-HXwhich, again, is cooled to the ambient. The resulting pressure drop induces the evaporation in theevaporator at about 20 ◦C, which is used to supply the air cooling of the server rooms. For continuousprovision of cooling, two Ad-HXs are operated alternately. In contrast to typical thermally drivencooling applications, the coefficient of performance (COP) of this cycle is determined by the ratio ofCPU and auxiliary heat loads and in the order of 0.5–0.6 [6].

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HX which, again, is cooled to the ambient. The resulting pressure drop induces the evaporation in the evaporator at about 20 °C, which is used to supply the air cooling of the server rooms. For continuous provision of cooling, two Ad-HXs are operated alternately. In contrast to typical thermally driven cooling applications, the coefficient of performance (COP) of this cycle is determined by the ratio of CPU and auxiliary heat loads and in the order of 0.5–0.6 [6].

Figure 1. Working principle of an adsorption chiller for data centre cooling with typical feed and return temperature levels (schematic): high temperature CPU waste heat is yielded by direct water cooling and used to drive the adsorption chiller cycle, the chiller provides low temperature cooling for less temperature stable auxiliary loads (e.g., hard disks, power supplies), all heat flows are rejected at medium temperature level to the ambient, e.g., through a cooling tower.

The development of new adsorbent materials has been a research interest for many years [8]. Aluminium fumarate, a metal-organic framework (MOF) that attracted increasing interest for thermal applications in recent years, exhibits adsorption equilibrium properties that fit well to the boundary conditions of this cycle [9]. Due to its beneficial stepwise isotherm [8], it can allow considerably more efficient cycles compared to the state-of-the-art material silica gel with a good hydrothermal cycle stability [10,11]. Under the temperature conditions depicted in Figure 1, aluminium fumarate undergoes the full uptake step of about 0.3 kg/kg [10], compared to little more than 0.1 kg/kg for silica gel. This advantage may be used to reduce the amount of adsorbent or to increase the power density by, e.g., shorter cycles [12]. The material is potentially a low-cost material due to widely available educts (Al-salts and fumaric acid) and a water-based synthesis route [13].

The increase in volume specific cooling power (VSCP)—thus the reduction in specific costs—while keeping a reasonably high COP, is one of the major development challenges for adsorption chillers [12]. Typical values for COPs of market-available adsorption chillers are in the order of 0.5 to 0.65 [14]. In the case of data centre cooling, the target COP is determined by the ratio of low temperature cooling demand and available waste heat from CPUs, which typically is in the same range [6]. A promising approach to increase VSCP is to use binder-based adsorbent coatings to allow for a substantially better heat transfer to the heat exchanger structure, in comparison to a loose grain bed, the state-of-the-art solution [15]. Further performance increase can be reached through model-

Figure 1. Working principle of an adsorption chiller for data centre cooling with typical feed andreturn temperature levels (schematic): high temperature CPU waste heat is yielded by direct watercooling and used to drive the adsorption chiller cycle, the chiller provides low temperature cooling forless temperature stable auxiliary loads (e.g., hard disks, power supplies), all heat flows are rejected atmedium temperature level to the ambient, e.g., through a cooling tower.

The development of new adsorbent materials has been a research interest for many years [8].Aluminium fumarate, a metal-organic framework (MOF) that attracted increasing interest for thermalapplications in recent years, exhibits adsorption equilibrium properties that fit well to the boundaryconditions of this cycle [9]. Due to its beneficial stepwise isotherm [8], it can allow considerablymore efficient cycles compared to the state-of-the-art material silica gel with a good hydrothermalcycle stability [10,11]. Under the temperature conditions depicted in Figure 1, aluminium fumarateundergoes the full uptake step of about 0.3 kg/kg [10], compared to little more than 0.1 kg/kg for silicagel. This advantage may be used to reduce the amount of adsorbent or to increase the power densityby, e.g., shorter cycles [12]. The material is potentially a low-cost material due to widely availableeducts (Al-salts and fumaric acid) and a water-based synthesis route [13].

The increase in volume specific cooling power (VSCP)—thus the reduction in specific costs—whilekeeping a reasonably high COP, is one of the major development challenges for adsorption chillers [12].Typical values for COPs of market-available adsorption chillers are in the order of 0.5 to 0.65 [14]. In thecase of data centre cooling, the target COP is determined by the ratio of low temperature cooling demandand available waste heat from CPUs, which typically is in the same range [6]. A promising approach toincrease VSCP is to use binder-based adsorbent coatings to allow for a substantially better heat transferto the heat exchanger structure, in comparison to a loose grain bed, the state-of-the-art solution [15].Further performance increase can be reached through model-based design and optimisation, which is

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more cost-effective than empiric trial-and-error prototyping, as shown recently in a comprehensiveoverview on designing strategies for Ad-HX by Graf et al. [16]. However, model-based design requiresdetailed knowledge of (a) the adsorption equilibria, (b) the adsorption enthalpy, (c) relevant physicalheat and mass mechanisms and the corresponding transfer coefficients, and (d) the specific heatcapacities, allowing for models with explicit dependency on design parameters like heat exchangergeometry, layer thicknesses and particle sizes. We developed a comprehensive approach to gain mostof this data, i.e., (a)–(c), from small representative Ad-HX cut-outs in a single measurement procedurebased on:

1. Volumetric uptake measurement;2. Stepwise volume and temperature perturbation;3. Frequency response analysis.

In this paper, we will focus on the first two steps for evaluating adsorption equilibrium andadsorption enthalpy. The frequency response analysis (FRA) for the investigation of heat and masstransfer processes builds upon this and will be dealt with in a following publication.

An apparatus developed initially for volume swing frequency response measurement also allowsfor measurements of the differential adsorption equilibrium, i.e., the slopes of the isotherm and the isobar,through the equilibrium response for small step experiments. Earlier, the FRA setups were used forvolume step experiments to evaluate sorption dynamics, using a numerical non-linear transport modelin the time domain [17], comparable to pressure jump [18,19] or temperature jump [20–22] experiments.We extend this approach to measuring the isobar slope with small temperature steps. Both slopes canbe directly combined to determine the differential adsorption enthalpy at a specific thermodynamicstate, i.e., adsorbent loading, temperature, and pressure. In combination with a calibrated dosingvolume for the volumetric uptake measurement, this allows for a comprehensive determination ofsorption equilibrium, enthalpy, and dynamics in a single automated measurement procedure.

2. Materials and Methods

2.1. Material

An aqueous dispersion (26.8 wt% aluminium fumarate (a.k.a. MIL-53(Al)-FA), Basolite® A520,BASF; 17.9 wt% SilRes® MP50E, Wacker Silicones) was processed by a knife coating applicator on50 × 50 × 2 mm AlMg3 sample plates (Table 1). The wet film thickness was varied by an octagonalstainless-steel mask with a defined thickness (200 µm, 350 µm, 600 µm) and constant coating surfaceAct (18.7 cm2). Samples were oven dried at 200 ◦C for 3 h before measuring coating thicknesses dct offinal samples (Table 1, Figure 2) at five points with a probe indicator. The composite dry mass mcmp wasdetermined by quickly (T ≥ 160 ◦C) weighing the hot samples under lab atmosphere after oven drying.Total dry adsorbent content ws,dry was first calculated from the suspension composition, based onexperimentally determined dry masses of different components, as shown by Kummer et al. [23],and later cross checked by comparing the samples’ uptake to the uptake of pure adsorbent powdermeasured volumetrically (AUTOSORB®, Quantachrome).

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based design and optimisation, which is more cost-effective than empiric trial-and-error prototyping, as shown recently in a comprehensive overview on designing strategies for Ad-HX by Graf et al. [16]. However, model-based design requires detailed knowledge of a) the adsorption equilibria, b) the adsorption enthalpy, c) relevant physical heat and mass mechanisms and the corresponding transfer coefficients, and d) the specific heat capacities, allowing for models with explicit dependency on design parameters like heat exchanger geometry, layer thicknesses and particle sizes. We developed a comprehensive approach to gain most of this data, i.e., a)–c), from small representative Ad-HX cut-outs in a single measurement procedure based on:

1. Volumetric uptake measurement; 2. Stepwise volume and temperature perturbation; 3. Frequency response analysis. In this paper, we will focus on the first two steps for evaluating adsorption equilibrium and

adsorption enthalpy. The frequency response analysis (FRA) for the investigation of heat and mass transfer processes builds upon this and will be dealt with in a following publication.

An apparatus developed initially for volume swing frequency response measurement also allows for measurements of the differential adsorption equilibrium, i.e., the slopes of the isotherm and the isobar, through the equilibrium response for small step experiments. Earlier, the FRA setups were used for volume step experiments to evaluate sorption dynamics, using a numerical non-linear transport model in the time domain [17], comparable to pressure jump [18,19] or temperature jump [20–22] experiments. We extend this approach to measuring the isobar slope with small temperature steps. Both slopes can be directly combined to determine the differential adsorption enthalpy at a specific thermodynamic state, i.e., adsorbent loading, temperature, and pressure. In combination with a calibrated dosing volume for the volumetric uptake measurement, this allows for a comprehensive determination of sorption equilibrium, enthalpy, and dynamics in a single automated measurement procedure.

2. Materials and Methods

2.1. Material

An aqueous dispersion (26.8 wt% aluminium fumarate (a.k.a. MIL-53(Al)-FA), Basolite® A520, BASF; 17.9 wt% SilRes® MP50E, Wacker Silicones) was processed by a knife coating applicator on 50 × 50 × 2 mm AlMg3 sample plates (Table 1). The wet film thickness was varied by an octagonal stainless-steel mask with a defined thickness (200 µm, 350 µm, 600 µm) and constant coating surface 𝐴ct (18.7 cm2). Samples were oven dried at 200 °C for 3 hours before measuring coating thicknesses 𝑑ct of final samples (Table 1, Figure 2) at five points with a probe indicator. The composite dry mass 𝑚 was determined by quickly (𝑇 160 °C) weighing the hot samples under lab atmosphere after oven drying. Total dry adsorbent content 𝑤 , was first calculated from the suspension composition, based on experimentally determined dry masses of different components, as shown by Kummer et al. [23], and later cross checked by comparing the samples’ uptake to the uptake of pure adsorbent powder measured volumetrically (AUTOSORB®, Quantachrome).

Figure 2. Sample Ct_610 with 0.61 mm coating thickness. Figure 2. Sample Ct_610 with 0.61 mm coating thickness.

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Table 1. Sample mass and geometry, the adsorbent content was estimated when mixing the coatingsuspension and confirmed later by comparing the sample’s uptake with the pure adsorbent powderisotherm (c.f. Section 3.1).

By SuspensionComposition

By Comparison to PureAdsorbent Uptake

Sample mcmp(mg) dct(mm) ρcmp (g/cm3) ws,dry(-) wbnd(-) ws,dry (-) wbnd(-)

Ct_140 134 ± 3 0.14 ± 0.04 0.51 ± 0.15 0.75 0.25 0.72 0.28Ct_240 217 ± 4 0.24 ± 0.05 0.48 ± 0.10 0.75 0.25 0.79 0.21Ct_610 563 ± 11 0.61 ± 0.07 0.49 ± 0.06 0.75 0.25 0.80 0.20

2.2. Apparatus

Measurements are performed with a custom setup (Figure 3, Table 2) under pure water vapouratmosphere, allowing vapour dosing as well as small volume and temperature steps. Moreover,the setup allows frequency response (FR), large temperature jump (LTJ), large pressure jump (LPJ) andsmall pressure jump (SPJ) experiments with water. Details on jump experiments with the setup havebeen reported extensively before [20,24,25], FR experiments will be published elsewhere.

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Figure 3. Sorption kinetic setup for frequency response, large temperature jump and large pressure jump experiments with absolute and differential equilibrium measurement. Absolute sorption equilibria are measured volumetrically by dosing in from the dosing chamber, differential equilibria by small temperature and pressure steps around equilibrium.

2.3. Procedure

The measurement procedure consists of two steps: pre-conditioning to the desired state and determination of equilibrium slopes. Throughout the measurement, the temperature-controlled cabinet is kept at the measurement mean temperature 𝑇 .

Initially, samples were desorbed against a rotary vane pump (𝑝 < 0.01 mbar) at 95 °C overnight, to remove any co-adsorbed impurities. For aluminium fumarate this ensures an initial loading 𝑋 of 0 kg/kg. After cooling down the closed chamber to 𝑇 , the sample is pre-conditioned to a desired loading 𝑋 by dosing in vapour from the dosing chamber. 𝑋 is calculated volumetrically from the mass balance of both chambers and the adsorbent dry mass 𝑚 = 𝑤 , 𝑚 following the ideal gas law, which is a very good approximation for water in the pressure and temperature region of the measurements:

𝑋 = 𝑋 + 1𝑇 𝑅 𝑚 𝑉 𝑝 + 𝑉 𝑝 − (𝑉 𝑝 + 𝑉 𝑝 ) . (1)

Here, indexes D and M denote the dosing and the measurement chamber where the volume depends on the bellow position, and indexes 1 and 2 denote the equilibrium state before and after dosing in vapour. The pressures 𝑝 , and 𝑝 , are calculated beforehand based on the isotherm of the pure adsorbent powder to approximately reach the set point for 𝑋 . The equilibrium pressure of the sample 𝑝 = 𝑝 , will follow the equilibrium of the sorbent at 𝑇 and 𝑋 , yielding a point on the 𝑇 -isotherm. To calculate the effective loading 𝑋 , the composite mass, 𝑚 is used in Equation (1) instead of 𝑚 .

To determine the equilibrium slopes at the pre-conditioned sample state, the sample is exposed to small volume and temperature jumps symmetrically around 𝑉 and 𝑇 , first by Δ𝑉 = 2𝑉 with constant temperature and then by Δ𝑇 = 4 K with constant volume. This allows determining the differential equilibrium, i.e., the slopes of the isotherm d𝑋/d𝑝 ≈ (Δ𝑋/Δ𝑝) and the isobar d𝑋/d𝑇 ≈

V2V3

V4

Vacuum pump

Dosing chamber

Measuring chamber

Thermostated cabinet

Vaporgenerator MExcenter MotorBellow

T3

PT

LV1Sample

T2T1 HV2HV1

Figure 3. Sorption kinetic setup for frequency response, large temperature jump and large pressure jumpexperiments with absolute and differential equilibrium measurement. Absolute sorption equilibriaare measured volumetrically by dosing in from the dosing chamber, differential equilibria by smalltemperature and pressure steps around equilibrium.

Table 2. Principal characteristics of measurement quantities, details are explained in the text.

Quantity Range Typical Uncertainty Device

Chamber volume 849–922 mL 0.4 mL (20 ◦C),1.3 mL (80 ◦C)

Schreiber Messtechnik LVDT

Chamber pressure 0–100 mbar 0.05 mbar (5 mbar),0.15 mbar (100 mbar)

MKS Baratron 627B

Cold plate temperature 20–95 ◦C 0.1 K 4-wired Pt100Sample surface temperature 20–80 ◦C Not applicable 1 Heitronics KT15

1 The sample surface temperature is used to qualitatively ensure steady state conditions.

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The volume of the dosing chamber is constant (VD = 41.815± 0.021 L), while the measurementchamber volume (VM = 885.4 ± 1.3 mL) can be varied by 4.12% through a mechanically drivenvacuum bellow, while the bellow position is recorded with a vacuum stable linear variable differentialtransformer (LVDT, Schreiber Messtechnik). The bellow position has been calibrated with a secondorder polynomial to the chamber volume by filling the evacuated and temperature-controlled chamberwith water of known mass. The sample is thermally well connected (thermal grease TG20032) to thecold plate kept isothermal (±0.01 K) by two switchable external circuits. The cold plate temperature isprecisely measured with a 4-wired Pt100 sensor embedded in a bore. The chamber pressure is measuredwith a capacitive pressure transducer (MKS Baratron 627B, 0–100 mbar). Additionally, the sample’ssurface temperature is recorded using an IR temperature sensor (Heitronics KT15) through a ZnSevacuum viewport with a noise equivalent temperature difference of 25 mK at a response time of 1 s.The measurement spot has a diameter of 6 mm (95%) and the detector’s spectral response maximumis between 8 and 14 µm, fitting to the transmissivity of the ZnSe viewport and the aimed sampletemperature (20–80 ◦C). To minimise temperature gradients, the whole vacuum setup is encapsulatedin a temperature-controlled cabinet (±0.1 K) set to the mean cold plate temperature. Data acquisition isperformed with a high precision digital multimeter (Agilent 34970A).

2.3. Procedure

The measurement procedure consists of two steps: pre-conditioning to the desired state anddetermination of equilibrium slopes. Throughout the measurement, the temperature-controlled cabinetis kept at the measurement mean temperature T0.

Initially, samples were desorbed against a rotary vane pump (p < 0.01 mbar) at 95 ◦C overnight,to remove any co-adsorbed impurities. For aluminium fumarate this ensures an initial loading Xinit

of 0 kg/kg. After cooling down the closed chamber to T0, the sample is pre-conditioned to a desiredloading X0 by dosing in vapour from the dosing chamber. X0 is calculated volumetrically from themass balance of both chambers and the adsorbent dry mass ms = ws,drymcmp following the ideal gaslaw, which is a very good approximation for water in the pressure and temperature region of themeasurements:

X0 = Xinit +1

T0Rwms[VDpD1 + VM1pM1 − (VM2pM2 + VDpD2)]. (1)

Here, indexes D and M denote the dosing and the measurement chamber where the volumedepends on the bellow position, and indexes 1 and 2 denote the equilibrium state before and afterdosing in vapour. The pressures pD,1 and pD,2 are calculated beforehand based on the isotherm ofthe pure adsorbent powder to approximately reach the set point for X0. The equilibrium pressure ofthe sample p0 = pM,2 will follow the equilibrium of the sorbent at T0 and X0, yielding a point on theT0-isotherm. To calculate the effective loading Xeff, the composite mass, mcmp is used in Equation (1)instead of ms.

To determine the equilibrium slopes at the pre-conditioned sample state, the sample is exposedto small volume and temperature jumps symmetrically around V0 and T0, first by ∆V = 2V withconstant temperature and then by ∆T = 4 K with constant volume. This allows determiningthe differential equilibrium, i.e., the slopes of the isotherm dX/dp ≈ (∆X/∆p)T and the isobardX/dT ≈ ((∆X − dX/dp∆p)/∆T)V from the equilibrium pressure difference ∆p and loading change∆X, measured for the isothermal and the isochoric jump, respectively. A very slow drift in the pressure,which is due to parasitic effects of the setup already reported [24,25], is corrected by fitting linearmodels to equilibrium sections before and after the jump and using the extrapolated values at thecentre. Finally, with both slopes the differential enthalpy of adsorption at X0 and T0 can be calculatedbased on the Clausius–Clapeyron equation assuming ideal gas behaviour:

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∆hs ≈RT2

pdpdT

= −RT2

pdXdT

(dXdp

)−1

(2)

Loading, differential equilibrium and adsorption enthalpy are important input parameters fora subsequent FRA reported elsewhere. Integration in a single measurement routine allows formeasurement under exactly the same conditions (in-situ). As the sample is pre-conditioned only once,this eliminates the need for time consuming external measurements and possibly error-prone transferto the measurement conditions.

To exclude a local hysteresis of the adsorption equilibrium, an important pre-requisite for FRA,a further test is included in the routine: The same equilibrium state X0, T0 is reached coming froma smaller and a larger volume at constant temperature and vice versa. The equilibrium loading isthen compared and a “hysteresis-free” behaviour assumed if the loading difference between the twodirections is below the measurement uncertainty.

2.4. Uncertainty Evaluation

Uncertainty analysis has been carried out based on GUM [26], including uncertainty from samplevariance (type A) and uncertainties from imperfect calibration and correction (type B).

The uncertainty of the mean values are between 0.4 mL (20 ◦C) and 1.3 mL (80 ◦C) for V0, between0.05 mbar (p0 = 5 mbar) and 0.15 mbar (p0 = 100 mbar) for the chamber pressure, and about 0.1 K forthe mean sample temperature T0. Typical uncertainties for vapour dosing are in the order of 1 to 4 mginfluenced mainly by p0 for 10 to 60 mbar. Thus, uncertainties for the loading are smaller for highersample dry mass, given constant dry mass uncertainty.

3. Results and Discussion

Results are reported for five different loadings at 40 ◦C and one loading at 30 ◦C and60 ◦C, respectively.

3.1. Adsorption Equilibrium

The water isotherm of the adsorbent powder at 40 ◦C (Figure 4) shows the characteristic step-likeuptake to a plateau at 0.32 kg/kg and is in line with [11], or slightly lower than [10,27] previous results.The position of the step is temperature dependent with an inflection point at prel ≈ 0.25, 0.28 and 0.33for 30, 40 and 60 ◦C. Measured local isotherm slopes are in agreement with the tangent for 40 ◦C.The position of the uptake step is reproducible within the samples and shows a strong temperaturedependency that persists when applying a Dubinin transformation [28]. Hence, the assumption ofa temperature invariant characteristic curve is a strong simplification for aluminium fumarate andshould be applied with care. The exact position of the uptake step is an important information forapplication, as it determines the available driving forces and finally the resulting equipment power [3].

No significant hysteresis was observed, neither locally by the procedure explained before,in Section 2.3, nor globally. For the latter, the vapour dosing procedure was modified starting with asaturated sample (prel = 0.5, T = 40 ◦C, Xinit = 0.33 kg/kgs) and desorbing into the dosing chamber.The hysteresis found in previous results was probably due to incomplete equilibrium and/or porecondensation occurring at prel � 0.5, which was disregarded here due to the limited relevance for heattransformation applications.

The adsorbent content calculated by comparing the uptake of the sample to that of the powder(Figure 4, right), fits on average the values calculated at sample preparation (Table 1), showing thatthe binder has no significant influence on adsorption equilibrium. The results show good agreementbetween the two thicker samples and a slight deviation of the thinnest sample Ct_140, which could beexplained by a slightly lower adsorbent content of the coating. The difference to the uptake of thepure adsorbent can be explained by the inert binder/loss due to the coating process, differences in theproduction process and measurement uncertainty of the volumetric adsorption measurement.

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A general description of the measured sorption equilibrium for modelling purposes is given inthe Supplementary Material (S1).

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Figure 4. Effective loading 𝑋 and loading 𝑋 = 𝑋 /𝑤 , over relative pressure measured for samples Ct_140 (▲), Ct_240 (■), and Ct_610 (●) in comparison with the 40 °C isotherm of the pure adsorbent powder (+), adsorbent content 𝑤 , determined by uptake correction; grey lines: local equilibrium slope measured by small volume jumps.

No significant hysteresis was observed, neither locally by the procedure explained before, in Section 2.3, nor globally. For the latter, the vapour dosing procedure was modified starting with a saturated sample (𝑝 = 0.5, 𝑇 = 40 °C, 𝑋 = 0.33 kg/kgs) and desorbing into the dosing chamber. The hysteresis found in previous results was probably due to incomplete equilibrium and/or pore condensation occurring at 𝑝 ≫ 0.5, which was disregarded here due to the limited relevance for heat transformation applications.

The adsorbent content calculated by comparing the uptake of the sample to that of the powder (Figure 4, right), fits on average the values calculated at sample preparation (Table 1), showing that the binder has no significant influence on adsorption equilibrium. The results show good agreement between the two thicker samples and a slight deviation of the thinnest sample Ct_140, which could be explained by a slightly lower adsorbent content of the coating. The difference to the uptake of the pure adsorbent can be explained by the inert binder/loss due to the coating process, differences in the production process and measurement uncertainty of the volumetric adsorption measurement.

A general description of the measured sorption equilibrium for modelling purposes is given in the Supplementary Material (S1).

3.2. Adsorption Enthalpy

The calculated differential enthalpy of adsorption is 2.90 ± 0.05 MJ/kg (52.2 ± 1.0 kJ/mol) on average. The calculation with Equation (2) is based on either the local equilibrium slope indicated in Figure 5 or on a linear fit of the quasi-isosteric points (𝑋 ≈ 0.16 kg/kg) measured at 30, 40 and 60 °C. The Clausius–Clapeyron plot shows that local slopes coincide well with the multi-temperature fit, and so do the calculated enthalpies. Temperature and loading dependencies are negligible in the parameter range evaluated. The adsorption enthalpy is about 10%–15% higher than expected by a simple Dubinin approximation (sum of evaporation enthalpy at the same temperature and the adsorption potential 𝐴 = −𝑅𝑇 ln(𝑝 ) , [28]), which is in qualitative accordance to the observed temperature variance of the isotherm. Thus, the application of the concepts of a characteristic curve

Figure 4. Effective loading Xeff and loading X = Xeff/ws,dry over relative pressure measured forsamples Ct_140 (N), Ct_240 (�), and Ct_610 (•) in comparison with the 40 ◦C isotherm of the pureadsorbent powder (+), adsorbent content ws,dry determined by uptake correction; grey lines: localequilibrium slope measured by small volume jumps.

3.2. Adsorption Enthalpy

The calculated differential enthalpy of adsorption is 2.90 ± 0.05 MJ/kg (52.2 ± 1.0 kJ/mol) onaverage. The calculation with Equation (2) is based on either the local equilibrium slope indicatedin Figure 5 or on a linear fit of the quasi-isosteric points (Xeff ≈ 0.16 kg/kg) measured at 30, 40 and60 ◦C. The Clausius–Clapeyron plot shows that local slopes coincide well with the multi-temperaturefit, and so do the calculated enthalpies. Temperature and loading dependencies are negligible in theparameter range evaluated. The adsorption enthalpy is about 10–15% higher than expected by a simpleDubinin approximation (sum of evaporation enthalpy at the same temperature and the adsorptionpotential A = −RT ln(prel), [28]), which is in qualitative accordance to the observed temperaturevariance of the isotherm. Thus, the application of the concepts of a characteristic curve to describe thesorption equilibrium, and of the adsorption potential to describe the sorption enthalpy, results in arather crude approximation for the case of aluminium fumarate.

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to describe the sorption equilibrium, and of the adsorption potential to describe the sorption enthalpy, results in a rather crude approximation for the case of aluminium fumarate.

Figure 5. Left: Clausius–Clapeyron plot (𝑝 = 1 bar) with measured equilibrium points for different samples (▲ Ct_140, ■ Ct_240, ● Ct_610) and isostere slope calculated from measured local deviations (short grey lines) and linear fit of points with 𝑋 ≈ 0.16 kg/kg (- - -), uncertainties of 𝑇 and 𝑝 are bellow point size; Right: differential adsorption enthalpy calculated from isostere slopes of local equilibria and 0.2-kg/kg-fit over corrected loading with the evaporation enthalpy of water (- - -)

4. Conclusions

In this work we developed a novel method for in-situ measurements of sorption equilibria and enthalpy, in an apparatus dedicated to the sorption dynamic measurement. The method, based on dosing vapour from calibrated volumes and small temperature and volume steps around an equilibrium point, allows for direct measurements of the isobar’s and isotherm’s slope, tightly around a specific thermodynamic state. This allows extracting the loading and temperature dependency of the isostere’s slope and thus the sorption enthalpy.

The method was tested on samples coated with a composite of aluminium fumarate particles with Silres® as a binder, in different thicknesses (140–610 µm) at 30–60 °C and the entire loading range. The measured sorption equilibrium fits expectations from the pure adsorbent powder’s isotherm and the coating composition. The coating procedure did not alter the adsorption properties.

The measurement of the differential adsorption enthalpy was successfully verified by comparing the local slope of the isostere to the linear regression over the whole temperature range. The sorption enthalpy is 2.90 ± 0.05 MJ/kg (52.2 ± 1.0 kJ/mol) on average, with no significant dependency with either loading or temperature.

Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Section S1: General description of the sorption equilibrium of aluminium fumarate.

Author Contributions: Conceptualization, E.L. and G.F.; methodology, E.L.; software, E.L.; validation, G.F. and L.S.; formal analysis, E.L.; investigation, E.L.; resources, E.L.; data curation, E.L.; writing—original draft preparation, E.L.; writing—review and editing, G.F., L.S. and G.S.; visualization, E.L.; supervision, G.F., L.S. and G.S.; project administration, G.F.; funding acquisition, E.L., G.F., L.S. and G.S. All authors have read and agreed to the published version of the manuscript.

Figure 5. Left: Clausius–Clapeyron plot (p0 = 1 bar) with measured equilibrium points for differentsamples (N Ct_140, � Ct_240, • Ct_610) and isostere slope calculated from measured local deviations(short grey lines) and linear fit of points with Xeff ≈ 0.16 kg/kg (- - -), uncertainties of T and p are bellowpoint size; Right: differential adsorption enthalpy calculated from isostere slopes of local equilibria and0.2-kg/kg-fit over corrected loading with the evaporation enthalpy of water (- - -).

Energies 2020, 13, 3003 8 of 10

4. Conclusions

In this work we developed a novel method for in-situ measurements of sorption equilibria andenthalpy, in an apparatus dedicated to the sorption dynamic measurement. The method, based ondosing vapour from calibrated volumes and small temperature and volume steps around an equilibriumpoint, allows for direct measurements of the isobar’s and isotherm’s slope, tightly around a specificthermodynamic state. This allows extracting the loading and temperature dependency of the isostere’sslope and thus the sorption enthalpy.

The method was tested on samples coated with a composite of aluminium fumarate particleswith Silres® as a binder, in different thicknesses (140–610 µm) at 30–60 ◦C and the entire loading range.The measured sorption equilibrium fits expectations from the pure adsorbent powder’s isotherm andthe coating composition. The coating procedure did not alter the adsorption properties.

The measurement of the differential adsorption enthalpy was successfully verified by comparingthe local slope of the isostere to the linear regression over the whole temperature range. The sorptionenthalpy is 2.90 ± 0.05 MJ/kg (52.2 ± 1.0 kJ/mol) on average, with no significant dependency with eitherloading or temperature.

Supplementary Materials: The following are available online at http://www.mdpi.com/1996-1073/13/11/3003/s1,Section S1: General description of the sorption equilibrium of aluminium fumarate.

Author Contributions: Conceptualization, E.L. and G.F.; methodology, E.L.; software, E.L.; validation, G.F.and L.S.; formal analysis, E.L.; investigation, E.L.; resources, E.L.; data curation, E.L.; writing—original draftpreparation, E.L.; writing—review and editing, G.F., L.S. and G.S.; visualization, E.L.; supervision, G.F., L.S. andG.S.; project administration, G.F.; funding acquisition, E.L., G.F., L.S. and G.S. All authors have read and agreed tothe published version of the manuscript.

Funding: This work results widely from the PhD project of Eric Laurenz for which funding by Heinrich BöllStiftung is gratefully acknowledged. In addition, funding by BMBF for project WasserMod2 (FKZ 03ET1554A) isgratefully acknowledged.

Acknowledgments: The authors would like to thank Harry Kummer for supervising and Raffael Wolf for carryingout the sample preparation, Phillip Hügenell for performing the AUTOSORB® measurement, and Florian Tönniesfor implementing parts of the data processing program.

Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

AbbreviationsAd-HX Adsorber heat exchangerVariablesT Temperature (K)p Pressure (Pa)X Loading (kgadsorbed/kgsorbent,dry)Xeff Effective loading (kgadsorbed/kgcomposite,dry)V Volume (m3)A Surface area (m2), adsorption potential (J/kg), Amplitude (any unit)R Universal gas constant (J/(mol K))Rw Specific gas constant of water (J/(kg K))m Mass (kg)t Time (s)M Molar mass (kg/mol)∆hs Differential adsorption enthalpy (J/kgadsorbed)Indicesw Waters (Ad)sorbent, (ad)sorption0 Temporal mean valueD Dosing chamberM Measurement chamber

Energies 2020, 13, 3003 9 of 10

V At constant volumeT At constant temperaturech (Measurement) chambercmp Compositect Coatingrel Relative

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